I had read somewhere before that their support for this film was related to attempts around the time (after WW2) to disband the USMC and distribute their functions with the Army and Navy. However I can't remember the source of this claim, so I'm not sure if its true. Was their support for the movie an attempt to improve their public perception?
There were calls after WW2 to combine the USMC into the Army/Navy, but the National Security Act of 1947 ended that. The Marine Corps did, and still does, quite a bit to bring about positive attention. The link is to a USMC public affairs office specifically for Hollywood film makers; they'll help you make a film that makes the Marine Corps look good. In the words of Truman, "They have a propaganda machine that is almost equal to Stalin's."
For more about the USMC's history, look up First to Fight. It doesn't cover Sands of Iwo Jima specifically, but has a lot about Marine Corps mythology.